Global structural brain connectivity has been reported to be sex-dependent with women having increased interhemispheric connectivity (InterHc) and men having greater intrahemispheric connectivity (IntraHc). However, (a) smaller brains show greater InterHc, (b) larger brains show greater IntraHc, and (c) women have, on average, smaller brains than men. Therefore, sex differences in brain size may modulate sex differences in global brain connectivity. At the behavioural level, sex-dependent differences in connectivity are thought to contribute to men-women differences in spatial and verbal abilities. But this has never been tested at the individual level. The current study assessed whether individual differences in global structural connectome measures (InterHc, IntraHc and the ratio of InterHc relative to IntraHc) predict spatial and verbal ability while accounting for the effect of sex and brain size. The sample included forty men and forty women, who did neither differ in age nor in verbal and spatial latent components defined by a broad battery of tests and tasks. High-resolution T1-weighted and diffusion-weighted images were obtained for computing brain size and reconstructing the structural connectome. Results showed that men had higher IntraHc than women, while women had an increased ratio InterHc/IntraHc. However, these sex differences were modulated by brain size. Increased InterHc relative to IntraHc predicted higher spatial and verbal ability irrespective of sex and brain size. The positive correlations between the ratio InterHc/IntraHc and the spatial and verbal abilities were confirmed in 1000 random samples generated by bootstrapping. Therefore, sex differences in global structural connectome connectivity were modulated by brain size and did not underlie sex differences in verbal and spatial abilities. Rather, the level of dominance of InterHc over IntraHc may be associated with individual differences in verbal and spatial abilities in both men and women.